Assessment of reduced-order models in analysis of Floquet modes in an infinite periodic elastic layer

Abstract

A hierarchy of reduced-order models of wave propagation in a periodic elastic layer is used to study the periodicity-induced stop-band effects. At each approximation level, the eigenfrequency problem for a unit symmetric periodicity cell with appropriate boundary conditions is shown to be equivalent to the problem of identification of frequencies separating pass- and stop-bands. Factorization of eigenfrequency equations and of equations defining positions of pass- and stop-bands for individual Floquet modes is demonstrated. The difference between accuracy levels of reduced order models for homogeneous and periodic layers is highlighted and explained.